IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v79y2015i3p451-461.html
   My bibliography  Save this article

Cooperative games with homogeneous groups of participants

Author

Listed:
  • L. Hernández-Lamoneda
  • Francisco Sánchez-Sánchez

Abstract

We consider a class of games, which we call “groups’ games”, in which players are partitioned into classes within which players may be considered indistinguishable. We compute explicit formulas for some of the principal values restricted to these games. This is particularly useful for dealing with games with a large number of players where the usual formulas would be impractical (or impossible) to compute. We give several examples that illustrate how this idea may be applied to concrete situations. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • L. Hernández-Lamoneda & Francisco Sánchez-Sánchez, 2015. "Cooperative games with homogeneous groups of participants," Theory and Decision, Springer, vol. 79(3), pages 451-461, November.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:3:p:451-461
    DOI: 10.1007/s11238-014-9474-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-014-9474-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-014-9474-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, September.
    2. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    3. L. Hernández-Lamoneda & R. Juárez & F. Sánchez-Sánchez, 2007. "Dissection of solutions in cooperative game theory using representation techniques," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(3), pages 395-426, February.
    4. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    5. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    6. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu, Genjiu & Driessen, Theo S.H. & Sun, Hao & Su, Jun, 2013. "Consistency for the additive efficient normalization of semivalues," European Journal of Operational Research, Elsevier, vol. 224(3), pages 566-571.
    2. L. Hernández-Lamoneda & F. Sánchez-Sánchez, 2017. "Linear symmetric rankings for TU-games," Theory and Decision, Springer, vol. 82(4), pages 461-484, April.
    3. Borkotokey, Surajit & Kumar, Rajnish & Sarangi, Sudipta, 2015. "A solution concept for network games: The role of multilateral interactions," European Journal of Operational Research, Elsevier, vol. 243(3), pages 912-920.
    4. Surajit Borkotokey & Loyimee Gogoi & Dhrubajit Choudhury & Rajnish Kumar, 2022. "Solidarity induced by group contributions: the MI $$^k$$ k -value for transferable utility games," Operational Research, Springer, vol. 22(2), pages 1267-1290, April.
    5. Francisco Sanchez-Sanchez & Ruben Juarez & Luis Hernandez-Lamoneda, 2008. "Solutions without dummy axiom for TU cooperative games," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-9.
    6. Carreras, Francesc & Giménez, José Miguel, 2011. "Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions," European Journal of Operational Research, Elsevier, vol. 211(1), pages 148-159, May.
    7. Panfei Sun & Dongshuang Hou & Hao Sun & Theo Driessen, 2017. "Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 336-352, April.
    8. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.
    9. Michael Jones & Jennifer Wilson, 2010. "Multilinear extensions and values for multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 145-169, August.
    10. Panfei Sun & Dongshuang Hou & Hao Sun, 2022. "Optimization implementation of solution concepts for cooperative games with stochastic payoffs," Theory and Decision, Springer, vol. 93(4), pages 691-724, November.
    11. Tadeusz Radzik, 2017. "On an extension of the concept of TU-games and their values," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 149-170, August.
    12. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    13. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    14. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
    15. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    16. Cano Berlanga, Sebastian & Giménez Gómez, José M. (José Manuel) & Vilella Bach, Misericòrdia, 2015. "Enjoying cooperative games: The R package GameTheory," Working Papers 2072/247653, Universitat Rovira i Virgili, Department of Economics.
    17. Frondel Manuel & Kutzschbauch Ole & Sommer Stephan & Traub Stefan, 2017. "Die Gerechtigkeitslücke in der Verteilung der Kosten der Energiewende auf die privaten Haushalte," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 18(4), pages 335-347, November.
    18. Lukáš Adam & Tomáš Kroupa, 2017. "The intermediate set and limiting superdifferential for coalitional games: between the core and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 891-918, November.
    19. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    20. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:79:y:2015:i:3:p:451-461. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.